The floods have swept through the two countries in recent weeks, forcing more than 700,000 people to leave their homes and killing 450.
Christian charity Tearfund says it is concerned traffickers could try and take advantage of the disaster to remove children from their families.
Talking about a local farmer, Sudarshan Sathianathan, Tearfund's head of Asia region said: "Families like Khan's will face an uncertain future now that they have been displaced and lost their livelihoods, especially those who ran small businesses like farms or shops.
"We know from previous disasters, such as the Bihar floods in 2008, that opportunistic traffickers will take advantage of vulnerable families in the wake of disasters by offering to temporarily take their child to cities to find work and send back money.
"Out of desperation, families accept the offer, without realising that their child – some as young as six years old – will be sold into the sex industry or into child labour. In some extremely sad cases, they never see their child again."
The charity says most children who are trafficked in the world are taken from areas faced with conflict and natural disasters like flooding
Tearfund's local church partners are now warning vulnerable families of the child security dangers.